We report on single-short laser crystallization of Ge/Si multilayer stacks consisting of alternating amorphous nanosized films of silicon and germanium using near- and mid-infrared femtosecond and picosecond laser pulses. The phase composition of the irradiated stacks was investigated by the Raman scattering technique. Several non-ablative regimes of crystallization were found, from partial crystallization of germanium without intermixing the Ge/Si layers to complete intermixing of the layers with formation of GexSi1-x solid alloys. The roles of one- and two-photon absorption, thermal and non-thermal (ultrafast) melting processes, and laser-induced stresses in selective pico- and femtosecond laser annealing are analysed based on theoretical estimations and comparison with experimental data. It is concluded that, due to a mismatch of the thermal expansion coefficients between the adjacent stack layers, efficient explosive solid-phase crystallization of the Ge layers is possible at relatively low temperatures, well below the melting point. The possibility of ultrafast non-thermal phase transition in germanium in the studied regimes is also discussed.